Question: $ \left(\dfrac{125}{64}\right)^{-\frac{4}{3}}$
Explanation: $= \left(\dfrac{64}{125}\right)^{\frac{4}{3}}$ $= \left(\left(\dfrac{64}{125}\right)^{\frac{1}{3}}\right)^{4}$ To simplify $\left(\dfrac{64}{125}\right)^{\frac{1}{3}}$ , figure out what goes in the blank: $\left(? \right)^{3}=\dfrac{64}{125}$ To simplify $\left(\dfrac{64}{125}\right)^{\frac{1}{3}}$ , figure out what goes in the blank: $\left({\dfrac{4}{5}}\right)^{3}=\dfrac{64}{125}$ so $ \left(\dfrac{64}{125}\right)^{\frac{1}{3}}=\dfrac{4}{5}$ So $\left(\dfrac{64}{125}\right)^{\frac{4}{3}}=\left(\left(\dfrac{64}{125}\right)^{\frac{1}{3}}\right)^{4}=\left(\dfrac{4}{5}\right)^{4}$ $= \left(\dfrac{4}{5}\right)\cdot\left(\dfrac{4}{5}\right)\cdot \left(\dfrac{4}{5}\right)\cdot \left(\dfrac{4}{5}\right)$ $= \dfrac{16}{25}\cdot\left(\dfrac{4}{5}\right)\cdot \left(\dfrac{4}{5}\right)$ $= \dfrac{64}{125}\cdot\left(\dfrac{4}{5}\right)$ $= \dfrac{256}{625}$